The many-Hilbert-space approach to the measurement problem in quantum mechanics is applied to a typical ‘‘yes-no’’ experiment relative to two branch routes corresponding to mutually exclusive propositions. First, we reformulate the notion of wave-function collapse by measurement as a dephasing process between the two branch waves of an interfering particle (from our own point of view as opposed to the conventional Copenhagen interpretation). In this way, the concept of ‘‘wave-function collapse’’ is replaced by that of a statistically defined dephasing process. One of the most important points of this paper is the introduction of an order parameter ε that quantitatively describes the degree of decoherence. Its value ranges from ε=0 (which describes the case in which the two waves are perfectly coherent) to ε=1 (which describes the case in which coherence is totally lost); for this reason ε is named the ‘‘decoherence parameter.’’ In terms of this parameter we formulate a definite criterion to judge whether an instrument works well or not as a measuring apparatus. Then, we study the interaction between a microscopic particle and a macroscopic system (a detector), by modeling the macrosystem with a linear array of complex δ potentials, which undergo several kinds of statistical fluctuations. This leads us, under particular conditions, to the so-called wave-function collapse, which is attained in the limit ε=1. We also examine in some detail which kind of elastic and/or inelastic collisions can give the wave-function collapse. Some connections with recent experimental results in neutron interferometry and quantum optics are also stressed.

Methods used for the computation of the stopping power of high-atomic-number media to light and heavy nuclear fragments in un-ionized and completely ionized states are reasonably well developed. This is not the case for partially ionized states. We propose a method that bridges these two extremes and discuss applications of the method to α particles and fission fragments in uranium at extreme temperatures and densities.

K x-ray spectra of heliumlike vanadium and associated dielectronic satellite emission from lithiumlike, berylliumlike, and boronlike vanadium have been observed with a high-resolution crystal spectrometer from the Lawrence Livermore electron-beam ion trap. Measurements include dielectronic satellite spectra from the KLL, KLM, KLN, KLO, and KLP resonance. Many transitions are identified that are unresolved in plasma observations, and transition energies are measured with high accuracy. Comparisons of calculated and observed intensities of selected transitions show few differences.

The Stark width and shift of six Zn ii and six Cd ii spectral lines have been measured for the electron-density range of 1.0×${10}^{23–}$1.23×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$ and for an electron-temperature range of 23 000–33 000 K in a pulsed linear arc plasma discharge in ${\mathrm{SF}}_6$ and argon-helium mixture. Obtained Stark-width data were compared with the values calculated on the basis of various theoretical approaches.

In the analysis of laser-spectroscopic line shapes, velocity-changing collisions are accounted for by adding to the density-matrix equations-of-motion terms involving the direct collision kernel. The direct collision kernel is the probability density per unit time that an atom has a specific velocity after a collision, as a function of its velocity before the collision. If the collision partner’s velocity distribution is not thermal, however, the direct collision kernel alone does not completely characterize the effect of collisions. In such cases it is necessary to include terms involving the exchange collision kernel. The exchange kernel is the conditional probability density per unit time that the atom has a specific velocity after the collision as a function of its collision partner’s velocity before the collision. Both the direct and the exchange collision kernels are obtained from the linearized Boltzmann equation. We derive an expression for the exchange kernel in terms of the colliding-pair scattering cross section, and calculate the exchange kernel for hard-sphere collisions. Moreover, we propose a phenomenological exchange kernel similar to the Keilson-Storer direct kernel [J. Keilson and K. E. Storer, J. Appl. Math. 10, 243 (1952)] and compare it with the hard-sphere kernel. In an earlier paper [P. R. Berman, J. E. M. Haverkort, and J. P. Woerdman, Phys. Rev. A 34, 4647 (1986)], a connection was made between the collision kernels of laser spectroscopy and the collision integrals of classical transport theory. We expand on this earlier work by including the exchange collision kernel, and indicate how results from classical transport theory might be used in setting the parameters appearing in the phenomenological exchange kernel. We interpret an excitation-transfer experiment in terms of the exchange kernel.

The mixing of substates of an isolated Rydberg manifold (constant n,m) is studied using time-evolution matrices U(t,t0). Coherent mixing is effected by a linearly ramped electric field, F(t)=Ḟt. The spherical l basis, diabatic (hydrogenic) p basis, and adiabatic (nonhydrogenic) q basis are considered. In the linear Stark regime, the diabatic levels are coupled by F(t) through the atomic core, parametrized by quantum defects. The resulting adiabatic levels EqF in this model group into a submanifold degenerate at F=0 plus shifted levels split off from the adiabatic manifold. Analytical expressions for the q levels Eqτ and their coupling Γqq′τ are derived as a function of rescaled field or time τ. The time evolution of the levels' populations is studied first for the two-level case—the usual Landau-Zener effect (LZE)—which is generalized to a multilevel Landau-Zener effect (MLZE) for any n manifold. The matrices U(t,t0) are constructed in the Riemann product representation, including Magnus corrections up to fourth order. The probability Pq→q′(Vl) of making a transition from state q to q′ upon a one-way pass across the manifold depends on a single parameter Vl=[2μl2/(3Ḟn9)]1/2 (when one μl≠0). Numerical results for l=m=0 indicate that either diabatic (p→p′=p) or adiabatic (q→q′=q) transitions always predominate, no matter what the ramp rate Ḟ. Strong evidence supports the conjecture that outer diabatic transitions between edge states of a manifold obey Pndiab(V)=exp(-βnπV2) for l=m=0, with βn=1 for n=2 (the LZE) and βn≈lnn for n≫2 (the MLZE), and that a similar analytical result holds for arbitrary {μl} and m.

We give a general theoretical description of radiative forces on atoms in a monochromatic radiation field. The driven transition has a lower level consisting of several substates, and we consider the limit of low velocities and weak intensities. This situation comprises the schemes where cooling to temperatures below the Doppler limit is possible. After expressing the atomic dipole in terms of the polarizability tensor, we obtain an expression of the force as the sum of the radiation pressure, the dipole force, and a contribution from the gradient of the polarization. This latter contribution contains a part resulting from redistribution of photons between the plane waves that compose the field, and a part resulting from fluorescence. We express the average force and the momentum-diffusion tensor in terms of a closed evolution equation for the lower-state density matrix. We show by a scaling argument that in any case of cooling, the final temperature goes down linearly with the intensity, until the recoil limit is approached. The description is valid for a weak and monochromatic, but otherwise arbitrary field, and it allows for the presence of an external magnetic field, and of hyperfine splitting. It is applicable to cooling in one, two, or three dimensions. We give numerical results for the average force in a number of specific cases of two counterrunning plane waves.

The multielectron dissociative ionization of ${\mathrm{O}}_2$ has been studied using an intense picosecond laser at 610 and 305 nm in the ${10}^{13}$–${10}^{15}$ W/${\mathrm{cm}}^2$ laser intensity range. The excitation mechanisms producing multicharged dissociating molecular ions are determined from the kinetic energies and laser-intensity dependences of the atomic oxygen ions following the fragmentation of the molecule. Both at 305 and 610 nm, the multicharged atomic fragments (${\mathrm{O}}^{+}$,${\mathrm{O}}^{2+}$,${\mathrm{O}}^{3+}$,${\mathrm{O}}^{4+}$) are produced from parent molecular ions that are sequentially ionized as they dissociate. Moreover, the transitions occur at well-defined internuclear distances independent of the peak laser intensity. A comparison with previous results obtained on ${\mathrm{N}}_2$ and CO is discussed.

The radiative and Auger emissions in cascade (RAC) model constructed earlier [G. Omar and Y. Hahn, Phys. Rev. A (to be published)] is applied to the calculation of the final-charge-state distribution in the decay of ${\mathrm{Ar}}^{+}$(1s¯) with an initial 1s hole created by synchrotron irradiation. Experimental data of Church et al. [Phys. Rev. A 36, 2487 (1987)] are reasonably well reproduced, including the observed asymmetry in the final-state charge distribution. In addition to ${\mathrm{Ar}}^{+}$(1s¯), we have also considered the decay of the initial states ${\mathrm{Ar}}^{+}$(2s¯), ${\mathrm{Ar}}^{+}$(2p¯), and Ar(1s¯,4p). The higher charge states are underestimated by the RAC model, presumably due to the neglect of correlated multielectron processes in the present calculation.

A general formulation for calculating the recombination probability from a system consisting of many autoionizing states interacting with many continuum states is given. The formulation is applied to obtain the recombination probability from two continuum states coupled to an autoionizing state. Explicit expressions for various fundamental processes contributing to recombination probability are also given.

Starting with the canonical quantization procedure for the electromagnetic field inside an effective (linear or nonlinear) medium, we present a direct-space formulation of the theory of quantum optics. This approach does not use the conventional modal decomposition of the field, but relies on the electromagnetic momentum operator defined in terms of local electric- and magnetic-field operators. The momentum operator contains all the information on the spatial characteristics of the field, and can describe the translation of a short light pulse in a nonlinear medium, without a modal analysis of the pulse. Propagation is described through an operatorial wave equation that relates the temporal evolution of an electromagnetic pulse to its spatial progression. Through this equation, the direct-space approach to quantum optics can treat traveling-wave nonlinear-optical phenomena and, at the same time, account for their quantum statistics. The theory is applied to squeezed-light generation by the parametric down-conversion of a short laser pulse, as an illustration.

A tunable, high-intensity picosecond-dye-laser system has been employed with electron energy analysis to investigate the dynamics of (3+1) resonance-enhanced multiphoton ionization via various vibrational levels of the ${\mathit{B}}^1$${\mathrm{\Sigma }}_{\mathit{u}}^{+}$ and ${\mathit{C}}^1$${\mathrm{\Pi }}_{\mathit{u}}$ electronic states in ${\mathrm{H}}_2$. At the intensities studied [(0.2–6)×${10}^{13}$ W/${\mathrm{cm}}^2$], we find evidence for production of molecular ions in various vibrational levels; at the lower intensities the population distribution of final vibrational states varies with wavelength in a manner consistent with resonant enhancement at the three-photon level, followed by ionization into a vibrational level of ${\mathrm{H}}_2^{+}$ roughly predictable by a Franck-Condon analysis of ionization out of the C state. At higher intensities, there is a shift to increased population of lower vibrational states of ${\mathrm{H}}_2^{+}$, consistent with an ac Stark shift of the correspondingly lower vibrational levels of the C state into resonance with the three-photon energy of the laser. Clear evidence of direct dissociation of ${\mathrm{H}}_2$ followed by single-photon ionization of the excited H atom is observed as well. Above-threshold ionization of these two processes occurs readily. We also find that dissociative ionization is an increasingly important ionization pathway as the wavelength is increased. Finally, we see evidence of a fourth ionization pathway, which we tentatively assign to photoionization into a transient bound state created by the avoided crossing of the first repulsive electronic state of ${\mathrm{H}}_2^{+}$, ‖2p${\mathrm{\sigma }}_{\mathit{u}}$,n〉, with the single-photon-dressed ground state of ${\mathrm{H}}_2^{+}$, ‖1s${\mathrm{\sigma }}_{\mathit{g}}$,n+1〉.

Information theory allows us to make quantitative statements about the strength and nature of the correlations between systems. Application of this theory to the quantized electromagnetic field reveals a special role for the two-mode squeezed states. The nonclassical properties of these states arise from the intermode correlations, and we apply information-theoretic methods to determine the strength of the correlation between specific pairs of observables. This analysis leads to the important general result that for any correlated pure state a given pair of single-system observables contains at most only half the information about the correlations. We discuss the implications of this result for the distinction between classical and quantum systems.

Consider a functional Q[n] that scales homogeneously, Q[${\mathit{n}}_{\lambda }$]=${\lambda }^{\mathit{k}}$Q[n], where ${\mathit{n}}_{\lambda }$(r)=${\lambda }^3$n(λr). It is already known that Q[n] is related to its functional derivative, q([n];r)==δQ[n]/δn, by kQ[n] =-F${\mathit{d}}^3$r n(r)r⋅∇q([n];r). We here prove that q([n];r) is related to its functional derivative by kq([n];r)=-F${\mathit{d}}^3$r’n(r’)r’⋅∇’{δq([n];r) /δn(r’)}-r⋅∇q([n];r) and that there also exists a homo- geneouslike scaling relation for q([n];r): q([${\mathit{n}}_{\lambda }$];r)=${\lambda }^{\mathit{k}}$q([n];λr). In addition, δq([n];r)/δn(r’)=δq([n];r’)/δn(r) because q([n];r) is the functional derivative of Q[n]. Based upon these exact properties of q([n];r) it is proved that if a trial potential q¯([n];r) satisfies kQ[n]=-F${\mathit{d}}^3$r n(r)r⋅∇q¯([n];r) and δq¯([n];r)/δn(r’)=δq¯([n];r’)/δn(r), then kq([n];r)=-F${\mathit{d}}^3$r’n(r’)r’⋅∇’{δq¯([n]; r)/δn(r’)}-r⋅∇q¯([n];r). If q¯([n];r) further satisfies q¯([${\mathit{n}}_{\lambda }$];r)=${\lambda }^{\mathit{k}}$q([n];λr), we prove that q([n];r)=q¯([n];r), which means that q¯ is exact. Application of the theorem to density-functional theory is discussed.

In this paper, we study cooperative two-photon transitions in a system of two (nonoverlapping) atoms for two processes: two-photon spontaneous emission and two-photon resonance fluorescence. Expressions are obtained for the energy shifts and decay rates due to the interaction of the atoms with and via the field. The altered decay rates signal the existence of superradiance and subradiance in the two-atom system. The energy shifts of the single-excitation states are found to be proportional to ${\mathit{R}}^{\mathrm{-}6}$ for small atomic separations R, and to ${\mathit{R}}^{\mathrm{-}2}$ for large separations.

Strong-field autoionization induced by smooth laser pulses is studied to take into account the high-order ionization processes. A second-order differential equation of the amplitude of the ground state is derived. For some special laser pulses, which include all the exponential ones, analytical results may be obtained. As an example, the explicit results of ground-state population and the photoelectron spectrum are given for an exponentially switched-on cw pulse. The multipeak structure in the photoelectron spectrum is more obviously manifested in the high spectrum resulted from the high-order ionization processes.

The interaction of an atomic system with a single mode of a quantized electromagnetic field is investigated in the dipole approximation. Two approximations that are almost always made in this analysis are the neglect of the diamagnetic term in the Hamiltonian and the dropping of the rotating-wave approximation (RWA) terms that correspond to processes that do not conserve energy. Both approximations involve the neglect of terms that are of the same order of magnitude so that consistency demands that they be considered together. It is demonstrated that, in the dipole approximation, a minor modification of the usual application of quantum electrodynamics to any atomic system can exactly incorporate the effects of the diamagnetic term into a new frequency of the electromagnetic cavity mode; this frequency is slightly different from that of the empty cavity. This result is then applied to the specific case of a charged harmonic oscillator interacting with a single mode. For this simple model an analytic solution can then be found that includes the effects of the diamagnetic term and does not use the RWA. It is found that, for off resonance, the normal modes of the coupled system oscillate at shifted frequencies which are in agreement with the second-order perturbation-theory calculation of the Lamb shift. When the cavity mode is tuned to the atomic oscillator frequency, the perturbation-theory Lamb-shift calculation is no longer valid, and the exact solution derived in this paper predicts a resonant Lamb shift that is significantly larger than the off-resonant single-mode Lamb shift. Furthermore, the frequency spectrum is qualitatively changed from the single frequency of the free atomic system to a doublet spectrum. An analytic solution of this harmonic-oscillator problem can also be found when the RWA terms are dropped from the Hamiltonian. Comparison of the two solutions reveals that the RWA terms contribute a frequency shift of magnitude independent of the field intensity in the simple case of a charged harmonic oscillator.

When trajectories of the exact and RWA solutions are compared in phase space, it is found that one effect of the RWA terms is to lift a twofold degeneracy of the phase-space orbits that occurs when the RWA terms are neglected. The harmonic-oscillator problem has several features in common with the interaction of a two-level atom with a single quantized field mode. Both Hamiltonians exhibit inversion symmetry and hence have parity as a good quantum number. Both Hamiltonians contain RWA terms. When these RWA terms are neglected, both Hamiltonians have a new constant of motion that can be identified with the total number of excitations in the combined system.

We present results of Floquet calculations of rates and yields for ionization of atomic hydrogen, in its ground state, in the presence of a relatively weak high-frequency field and a relatively strong low-frequency (1064-nm) field. We assume that the two frequencies are incommensurable, or, if they are not, we average over the relative phase. We explore three processes: (i) Resonance-enhanced ionization, via levels that are ac-Stark mixed or/and very strongly shifted, (ii) laser-induced continuum structure, and (iii) nonresonant ionization in a regime where, despite the fact that the infrared field significantly shifts the ground state relative to the continuum, it only redistributes the photoelectrons over the low-frequency channels. We also illustrate the sensitivity of the ionization yield to the spatiotemporal configuration of the two fields.

We have studied the polarization properties of phase conjugation by degenerate four-wave mixing utilizing the 3S→4S two-photon-allowed transition of sodium. We have observed high-fidelity vector phase conjugation (simultaneous conjugation of the optical wave front and the state of polarization) at a reflectivity of ∼1% for the case where the states of polarization of the two counterpropagating pump waves were circular and counterrotating. High-fidelity polarization conjugation with high reflectivity was obtained only when the forward pump wave was much stronger than the backward pump wave. To explain these results, it is necessary to include the effects of grating washout due to atomic motion in the theoretical analysis.

The norm of the ground-state vector of a many-fermion system that is generated by the adiabatic theorem is examined in detail. A systematic way is presented to renormalize the state vector so that its norm would be conserved during the adiabatic development.